4 research outputs found
On polynomially integrable domains in Euclidean spaces
- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- 19/01/2017
- Field of study
Let D be a bounded domain in Rn, with smooth boundary. Denote
VD(ω,t), ω∈Sn−1,t∈R, the Radon transform of
the characteristic function χD of the domain D, i.e., the (n−1)−
dimensional volume of the intersection D with the hyperplane {x∈Rn:=t}. If the domain D is an ellipsoid, then the function
VD is algebraic and if, in addition, the dimension n is odd, then
V(ω,t) is a polynomial with respect to t. Whether odd-dimensional
ellipsoids are the only bounded smooth domains with such a property? The
article is devoted to partial verification and discussion of this question
Lecture 15: Semiclassical Limit; Coherent States; Metaplectic Group
- Publication venue
- 'Atlantis Press'
- Publication date
- Field of study
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- 'Elsevier BV'
- Publication date
- 01/01/2014
- Field of study
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- 'Elsevier BV'
- Publication date
- 01/01/1984
- Field of study